Why doesn't varus build Blade of the ruined king?

Because he's a poke adc. Q would do less damage if he had a Botrk instead of BT. Unless enemy team is stacking health then I'd stay away from Botrk imo.

He can build a BORK. He's being played as more of an AD caster than a traditional ADC role recently, which is why you see Manamune, etc. on him.

statwise botrk is inferior to bloodthirster. The active on it is nice for some champs, but the range is low. varus is an example of an adc that would enver want to get close enough to use the active, and he really cant kite, even if he uses the active.

You only generally build on champions with poor ad scaling in their abilities. Like